The planetary gear transmission has substantially replaced the fixed-axis gear train transmission in the field of high-efficiency transmissions. However, the primary restriction on further increase in the efficiency of planetary gear transmissions is the limited engagement efficiency of their fixed-axis gear pair and the significant power loss in their planetary bearings. Therefore, a significant advantage exists for an efficient planetary gear transmission having a low tooth number differential that also exhibits a high transmission ratio.
U.S. Pat. No. 3,451,290 to Wildhaber (Wildhaber '290) discloses a high-efficiency gear transmission drive comprising cases or housings, an input shaft and an output shaft. Bearings support a double-ring gear assembly comprised of two coaxial gear rings integrated with each other on an eccentric shaft. A gear ring is coaxially located concentrically and radially outside the double-ring gear assembly and has a different number of gear teeth than the outermost gear of the double-ring assembly. The gear transmission drive further comprises two fixed-axis gears. This construction reduces the load on the high-speed bearings. However, Wildhaber '290 does not discuss the mechanical parameters of these gears, the cooperative effects of which impact fundamentally on the operation of the gear transmission drive.
GB 1,198,737 to Morozumi (Morozumi '737) discloses an addendum modified involute internal gearing assembly including coaxially arranged external and internal gears. In order to improve the efficiency of the gearing, Morozumi '737 suggests that the difference of the addendum modification coefficients X.sub.2 and X.sub.1, respectively, of the internal gear and the external gear shall satisfy the following formula, hereinafter known as Formula (1): EQU [0.0002 (.alpha..sub.c).sup.2 -0.025 .alpha..sub.c +1.52]h.sub.k +0.8X.sub.1 &gt;X.sub.2 &gt;Kh.sub.k +X.sub.1
wherein .alpha..sub.c is standard pressure angle, h.sub.k is the addendum coefficient and K is 1 when the difference in tooth numbers between the gears is 1 and a function of .alpha..sub.c when the tooth number differential is 2.
In the prior art, including Morozumi '737, .xi..sub..alpha. .gtoreq.1 is required for resolving the contradiction of the contact ratio and the interference of an involute internal gear pair having a low tooth number differential. This is because rather than face contact ratio .xi..sub..beta. ##EQU1## wherein B is the width of tooth, .beta. is the reference helix angle, .pi.=3.1416, and m is the normal module, (m is a standard module when the gear is helical) only the profile contact ratio .xi..sub..alpha. (or .xi. as shown in Morozumi '737) is taken into account. That is to say, .xi..sub..alpha. has a close relationship with addendum coefficient ha (or "h.sub.k " as shown in Morozumi '737, ha equals the ratio between the addendum and the module), but .xi..sub..beta. has nothing to do with the addendum coefficient. In the situation (as in Morozumi '737) wherein only equation .xi..sub..alpha. .gtoreq.1 is considered, ha cannot be greatly reduced, hence a larger difference of addendum modification coefficients X (X=X.sub.2 -X.sub.1, where X.sub.1 is the addendum modification coefficient of the external gear and X.sub.2 is the addendum modification coefficient of the internal gear when the gear pair is an internal one, or X.sub.1 and X.sub.2 are the addendum modification coefficients of the two gears respectively when the gear pair is an external one) is used to offset the larger ha. As a result, the angle of engagement is larger, thus exacerbating engagement inefficiency and bearing loss. For example, Morozumi '737 defines that .xi..sub..alpha. &gt;1, even .xi..sub..alpha. &gt;2. Under such premise, for the formula put forward in Morozumi '737 (see Formula (1) described above), in order to satisfy the interference condition for correct engagement of an involute internal gear pair having reduced tooth number differential, by adjusting the parameters X.sub.1, X.sub.2, h.sub.k and .alpha..sub.c, a large X should be used, thus reducing the drive efficiency.
The present invention has gone beyond the known definition .xi..sub..alpha. .gtoreq.1 for an involute internal gearing pair having a low tooth number differential, e.g., 6 or less, and provides that .xi..sub..alpha. &lt;1 may be used on condition that .xi..sub..alpha. &gt;0 and .xi..sub..upsilon. =.xi..sub..alpha. +.xi..sub..beta. .gtoreq.1 or even .xi..sub..upsilon. =.xi..sub..alpha. +.xi..sub..beta. .gtoreq.0.7. Since face contact ratio .xi..sub..beta. is meaningful in relationship only to reference helix angle .beta., tooth width B and module m, and since it has nothing to do with ha, an increase of .xi..sub..beta. does not affect a reduction of ha. As a result, ha may be greatly reduced until ha=0.06 to 0.2 (when tooth number difference Zd=1). Therefore, the problem of interference is resolved without increasing the difference in addendum modification coefficients X, and a relation .vertline.X.vertline.&lt;0.1 or even X=0 may be allowed. Therefore, engagement and transmission efficiency are increased and bearing loss is reduced.
Morozumi '737, on the other hand, defines that .xi..sub..alpha. &gt;1. For meeting the requirement that no interference occur, according to Formula (1) described above, the addendum coefficient hk is difficult to reduce to less than 0.6 (when Zd is equal to 1 or 2), and the difference in addendum modification coefficients X is difficult to reduce to less than 0.5. By contrast, however, the present invention may satisfy that ha &lt;0.5, .vertline.X.vertline.&lt;0.1, or even X=0. Since Formula (1) of Morozumi '737 does not define k when the difference in tooth number Zd is not 1, so X=X.sub.2 -X.sub.1 &gt;kh.sub.k that formula has little substantive meaning when Zd is other than 1. When the difference in tooth number Zd is equal to 1, Morozumi 3 737 defines that K=1, so X.sub.2 &gt;h.sub.k +X.sub.1 or X.sub.2 -X.sub.1 &gt;hk or X.gtoreq.h.sub.k are obtained. It is necessary to point out that when difference in teeth numbers Zd is equal to 1, under the condition that the gears are straight spur gears (.beta.=0), .xi..sub..beta. &gt;1, and there is no interference (which is defined in Morozumi '737), the preferred scope of parameters for increasing the efficiency are that X=0.5 to 0.55, ha=0.55 to 0.6, i.e. 0.5&lt;X&lt;h.sub.k &lt;0.6 (wherein h.sub.k is ha) and X=h.sub.k -0.05. Thus, Formula (1) of Morozumi '737 cannot exist in effective scope to reduce .vertline.X.vertline.&lt;0.5 as it is confined by the interference condition.